Red queen for a day: models of symmetry and selection in paleoecology

Abstract

The Unified Theory of Biodiversity (UNTB), the Red Queen’s Hypothesis (RQH), and the Cascading Extinctions on Graphs hypothesis (CEG) are explored as members of a spectrum describing the ecological partitioning of species richness. All are models of historical biodiversity, but fare differently in explaining observed features of Phanerozoic biodiversity. The models treat species as symmetric, asymmetric, or partially symmetric respectively. Symmetry in the UNTB is broken by the generation and selection of variation of ecological performance, while the robustness and hence longevity of RQ communities are subject to selection. The CEG model reconciles some of the differences, demonstrating the importance of functional partitioning to both species evolution and selection at the community level. It is concluded that the UNTB explains communities partially on the shortest of evolutionary time scales, while RQ communities would be, at best, geologically ephemeral yet conditionally important.

Notes

Acknowledgments

Appendix

Number of partitions in a community

Let the number of species in the community/metacommunity be S. How many ways can S be partitioned ecologically? Reserving a minimum of one partition for primary producers (photosynthetic or otherwise), this leaves at most S − 1 species. All species could be assigned to a single partition, implying that they are either neutral in the UNTB sense, or share basic characteristics of their ecological interactions, as in the CEG model. Alternatively, each species could be considered as truly individual, yielding a maximum of S − 1 partitions. In reality, however, it is far likelier for the species to occupy a number of partitions between one and S − 1. The number of different ways in which these species can therefore be partitioned is calculated by considering the number of partitions possible at each integer ranging from one up to S − 1, and summing over the entire range,

The number of ways in which a community of species can be partitioned, with at least one partition reserved for primary production. Circles are values calculated according to binomial formulae in Eq. 1, while the solid curve is the Mersenne Number over all values (Eqs. 2, 3)